Simplify this trigonometric equation (identities)Please simplify these trigonometric identities and describe step by step (wording). sec ⁡ θ − csc ⁡ θ 1 − cot ⁡ θ

Question

Simplify this trigonometric equation (identities)Please simplify these trigonometric identities and describe step by step (wording).            sec      ⁡      θ      −      csc      ⁡      θ              1      −      cot      ⁡      θ

Savanna Smith · Accepted Answer

Change   sec  ⁡  θ   to   1      /    cos  ⁡  θ  ,  csc  ⁡  θ   to   1      /    sin  ⁡  θ  ,   and   cot  ⁡  θ   to   cos  ⁡  θ      /    sin  ⁡  θ so you have                    1                  c          o          s                      ϴ                              −              1                  s          i          n                      ϴ                                      1      −                        c          o          s                      ϴ                                    s          i          n                      ϴ                              Now multiply both the numerator and denominator of 1/cosϴ by sinϴ, the numerator and denominator of 1/sinϴ by cosϴ, and the numerator and denominator of 1 by sinϴ in order to add the two terms together (remember for fractions, if the denominators are equal, then just add the numerators together) so you have                              s          i          n                      ϴ                                    s          i          n                      ϴ                    c          o          s                      ϴ                              −                        c          o          s                      ϴ                                    s          i          n                      ϴ                    c          o          s                      ϴ                                                        s          i          n                      ϴ                                    s          i          n                      ϴ                              −                        c          o          s                      ϴ                                    s          i          n                      ϴ                              Now you just add the numerators so you have                    s        i        n                  ϴ                −        c        o        s                  ϴ                            s        i        n                  ϴ                c        o        s                  ϴ                                    s        i        n                  ϴ                −        c        o        s                  ϴ                            s        i        n                  ϴ                    Now dividing by a fraction is the same as multiplying by the reciprocal of it so the operation turns into            s      i      n              ϴ            −      c      o      s              ϴ                    s      i      n              ϴ            c      o      s              ϴ              ∗            s      i      n              ϴ                    s      i      n              ϴ            −      c      o      s              ϴ            Now you see that the numerator of the first term cancels with the denominator of the second term so you are left with            s      i      n              ϴ                    s      i      n              ϴ            c      o      s              ϴ            Now the sinϴ in the numerator cancels with the sinϴ in the denominator so you are left with      1          c      o      s              ϴ            Or simply  s  e  c      ϴ

Simplify this trigonometric equation (identities) Please simplify these trigonometric identities and describe step by step (wording). (sec theta-csc theta)/(1-cot theta)

Answered question

Answer & Explanation

New Questions in Trigonometry